# How do you factor 16x^2 - 8x - 15?

Jan 10, 2016

y = (4x + 3)(4x - 5)

#### Explanation:

I use the New AC Method to factor trinomials (Socratic Search)
$y = 16 {x}^{2} - 8 x - 15 =$16(x + p)(x + q) (1)
Converted trinomial: $y ' = {x}^{2} - 8 x - 240 =$ (x + p')(x + q') (2).
p' and q' have opposite signs.
Factor pairs of (ac = - 240) --> (-6, 40)(-8, 30)(-12, 20). This sum is: (20 - 12 = 8 = -b). The opposite sum (12, -20) gives: p' = 12 and q' = -20. Back to trinomial (1), $p = \frac{p '}{a} = \frac{12}{16} = \frac{3}{4}$ and $q = \frac{q '}{a} = - \frac{20}{16} = - \frac{5}{4.}$
Factored form: $y = 16 \left(x + \frac{3}{4}\right) \left(x - \frac{5}{4}\right) = \left(4 x + 3\right) \left(4 x - 5\right)$.
Check by development:
$\left(4 x + 3\right) \left(4 x - 5\right) = 16 {x}^{2} - 20 x + 12 x - 15 = 16 {x}^{2} - 8 x - 15$. OK